I think galleries should share the names. If they don't trust me, then why would they want to represent me. And if I don't trust them, why would I want them to represent me.
On my blog I have posted in the About Me section "I'm a painter living in Cincinnati, Ohio. If you are interested in purchasing any of my work, contact"...followed by the name of the gallery and the e-mail address. I think that is the best way to promote trust.